when you read a problem that has the word, "varies" we have the following general form
varies direct we have: y = kx
varies inversely we have: y = k/x = k(1/x)
varies jointly: y = kxy
You have a combined one with jointly and inversely so the general form is y = k(rq/t)
If you notice, a , "k" appears on the right side of the equal sign. This is called the constant of variation. Typically, in these problems they will give you an initial set of values and then you have to solve for k and then use another set of values to find y or one of the other variables. For example, if y varies directly as x when x = 12 and y = 36 what is y when x = 3. We solve it as follows
y = kx
now use the initial values of x = 12 and y = 36 and solve for k and we get
36 = k12
36 = 12k
3 = k
now the general form is
y = 3x
use this to solve the problem for y when x = 3 and we get
y = 3(3)
y = 9
Now with all that said let's get to your problem.
p = k(rq/t)
substitute in the values given initially and we get
Answers & Comments
when you read a problem that has the word, "varies" we have the following general form
varies direct we have: y = kx
varies inversely we have: y = k/x = k(1/x)
varies jointly: y = kxy
You have a combined one with jointly and inversely so the general form is y = k(rq/t)
If you notice, a , "k" appears on the right side of the equal sign. This is called the constant of variation. Typically, in these problems they will give you an initial set of values and then you have to solve for k and then use another set of values to find y or one of the other variables. For example, if y varies directly as x when x = 12 and y = 36 what is y when x = 3. We solve it as follows
y = kx
now use the initial values of x = 12 and y = 36 and solve for k and we get
36 = k12
36 = 12k
3 = k
now the general form is
y = 3x
use this to solve the problem for y when x = 3 and we get
y = 3(3)
y = 9
Now with all that said let's get to your problem.
p = k(rq/t)
substitute in the values given initially and we get
- 2 = k((4)(2))/(- 7)
14 = k8
14 = 8k
14/8 = k
7/4
so the general equation they are asking for is
p = 7/4(qr)/t